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Title:
A METHOD OF RESERVOIR COMPUTING AND A RESERVOIR COMPUTING SYSTEM
Document Type and Number:
WIPO Patent Application WO/2023/075601
Kind Code:
A1
Abstract:
The invention describes a method of reservoir computing and a reservoir computing system. A reservoir is provided which is operable to output an output signal in response to an input signal. The reservoir is provided with a reactor apparatus with a reactor chamber for receiving chemical substances and facilitating chemical reactions during a chemical process. An input layer is provided having at least one input node configured to receive the input signal; wherein the at least one input node is associated to one or more process parameters and/or a quantity of one or more chemical substances provided to the reactor chamber. Furthermore, a trained output layer is provided having at least one output node configured to output the output signal that is based on one or more readout outputs of the reservoir in response to the input signals.

Inventors:
HUCK WILHELMUS THEODORUS STEFANUS (NL)
BALTUSSEN MATHIEU GÉRARD (NL)
ROBINSON WILLIAM EDWARD (NL)
DE JONG THIJS (NL)
GHOSH SOUVIK (NL)
Application Number:
PCT/NL2022/050609
Publication Date:
May 04, 2023
Filing Date:
October 31, 2022
Export Citation:
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Assignee:
STICHTING RADBOUD UNIV (NL)
International Classes:
G06N3/00; G06N3/04; G06N3/06
Other References:
YAHIRO WATARU ET AL: "A reservoir computing approach for molecular computing", THE 2018 CONFERENCE ON ARTIFICIAL LIFE, 1 July 2018 (2018-07-01), pages 1 - 8, XP055908624
GOUDARZI ALIREZA ET AL: "DNA Reservoir Computing: A Novel Molecular Computing Approach", 22 September 2013, ADVANCES IN BIOMETRICS : INTERNATIONAL CONFERENCE, ICB 2007, SEOUL, KOREA, AUGUST 27 - 29, 2007 ; PROCEEDINGS; [LECTURE NOTES IN COMPUTER SCIENCE; LECT.NOTES COMPUTER], SPRINGER, BERLIN, HEIDELBERG, PAGE(S) 76 - 89, ISBN: 978-3-540-74549-5, XP047422689
GOUHEI TANAKA ET AL: "Recent Advances in Physical Reservoir Computing: A Review", ARXIV.ORG, CORNELL UNIVERSITY LIBRARY, 201 OLIN LIBRARY CORNELL UNIVERSITY ITHACA, NY 14853, 15 August 2018 (2018-08-15), XP081201048, DOI: 10.1016/J.NEUNET.2019.03.005
SEMENOV ET AL., NATURE CHEMISTRY, vol. 7, 2015, pages 160 - 165
SEMENOV ET AL., NATURE, vol. 537, 2016, pages 656 - 660
WONGHUCK, BEILSTEIN JOURNAL OF ORGANIC CHEMISTRY, vol. 13, 2017, pages 1486 - 1497
M.G. BALTUSSEN ET AL.: "A Bayesian Approach to Extracting Kinetic Information from Artificial Enzymatic Networks", ANALYTICAL CHEMISTRY, vol. 94, 2022, pages 7311 - 7318
SEMENOV, S. N. ET AL.: "Rational design of functional and tunable oscillating enzymatic networks", NAT. CHEM., vol. 7, 2015, pages 160 - 165
HAAS, M.LAMOUR, S.TRAPP, O: "Development of an advanced derivatization protocol for the unambiguous identification of monosaccharides in complex mixtures by gas and liquid chromatography", J. CHROMATOGR. A, vol. 1568, 2018, pages 160 - 167, XP085443693, DOI: 10.1016/j.chroma.2018.07.015
BECKER, M.LIEBNER, F.ROSENAU, T.POTTHAST, A.: "Ethoximation-silylation approach for mono- and disaccharide analysis and characterization of their identification parameters by GC/MS", TALANTA, vol. 115, 2013, pages 642 - 651, XP028720551, DOI: 10.1016/j.talanta.2013.05.052
BECKER, M. ET AL.: "Evaluation of different derivatisation approaches for gas chromatographic-mass spectrometric analysis of carbohydrates in complex matrices of biological and synthetic origin", J. CHROMATOGR. A, vol. 1281, 2013, pages 115 - 126, XP028981307, DOI: 10.1016/j.chroma.2013.01.053
HARRIS, C. R. ET AL.: "Array programming with NumPy", NATURE, vol. 585, 2020, pages 357 - 362, XP037247883, DOI: 10.1038/s41586-020-2649-2
"SciPy 1.0: Fundamental algorithms for scientific computing in Python", NAT METHODS, vol. 17, 2020, pages 261 - 272
LAINE, R. A.SWEELEY, C. C: "Analysis of trimethylsilyl O-methyloximes of carbohydrates by combined gas-liquid chromatography-mass spectrometry", ANALYTICAL BIOCHEMISTRY, vol. 43, 1971, pages 533 - 538, XP024821189, DOI: 10.1016/0003-2697(71)90284-3
MCKINNEY, WES: "Pandas: a foundational Python library for data analysis and statistics", PYTHON FOR HIGH PERFORMANCE AND SCIENTIFIC COMPUTING, vol. 14, no. 9, 2011, pages 1 - 9
PEDREGOSA, FABIAN ET AL.: "Scikit-learn: Machine learning in Python", THE JOURNAL OF MACHINE LEARNING RESEARCH, vol. 12, 2011, pages 2825 - 2830
Attorney, Agent or Firm:
WITMANS, H.A. (NL)
Download PDF:
Claims:
Claims 1. A method of characterizing an input signal, the method comprising the steps of: providing a reservoir which is operable to output an output signal in response to an input signal; wherein the reservoir is provided with a reactor apparatus with a reactor chamber for receiving chemical substances and facilitating chemical reactions during a chemical process; conducting a non-linear chemical process inside said reactor chamber by providing one or more chemical substances to said reactor chamber, wherein said non- linear chemical process comprises one or more chemical reactions; providing an input layer having at least one input node configured to receive the input signal; wherein the at least one input node is associated to one or more process parameters and/or a quantity of one or more chemical substances provided to the reactor chamber; and providing a trained computer implemented output layer having at least one output node configured to output the output signal that is based on one or more readout outputs of the reservoir in response to the input signals. 2. The reservoir computing method according to claim 1, wherein at least one input node is associated to a quantity of the one or more chemical substances in the reactor chamber at the start of the non-linear chemical process. 3. The reservoir computing method according to claim 1 or 2, wherein the reactor chamber is in fluid communication with a plurality of substance interface ports for transport of chemical substances towards said reactor chamber during the non-linear chemical process, and wherein at least one input node is associated to a quantity of the one or more chemical substances provided to the reactor chamber. 4. The reservoir computing method according to claim 3, wherein at least one of the one or more chemical substances provided to the reactor chamber is a catalyst.

5. The reservoir computing method according to claim 4, wherein at least two chemical substances are provided to said reaction chamber, wherein at least a first chemical substance is a first catalyst and at least a second chemical substance is a second catalyst, wherein the first catalyst influences at least one first chemical reaction, and wherein the second catalyst influences at least one second chemical reaction, wherein the at least one first and second chemical reactions are different. 6. The reservoir computing method according to any one of the preceding claims, wherein at least one input node is associated to one or more dynamic parameters of the one or more chemical substances provided to the reactor chamber. 7. The reservoir computing method according to claim 6, wherein the one or more dynamic parameters is one or more oscillation parameters, wherein preferably the oscillation parameter is an amplitude of substance quantity and/or a frequency of oscillation. 8. The reservoir computing method according to any one of the preceding claims, wherein the reactor has one or more adjustable process parameters, and wherein a first set of adjustable process parameters are connected to the at least one input node, and wherein the one or more process parameters includes: pressure inside the reactor chamber; a space velocity of the chemical substances in the reactor chamber; a pH value inside the reactor chamber; and/or a temperature inside the reactor chamber. 9. The reservoir computing method according to any one of the preceding claims, wherein the one or more readout outputs of the reservoir are based on measured values including: one or more process states; data indicative of a reactor chamber compound composition; a number of different compounds in the reactor chamber; a concentration of one or more compounds in the reactor chamber; and/or relative differences in concentrations of different compounds in the reactor chamber. 10. The reservoir computing method according to claim 9, wherein the one or more readout outputs of the reservoir are based on a rate of change of the measured values. 11. The reservoir computing method according to any one of the preceding claims, wherein the one or more chemical substances are selected from the group consisting of small organic compounds, proteins, synthetic polymers, and inorganic compounds. 12. The reservoir computing method according to any one of the preceding claims, wherein the non-linear chemical process comprises one or more recursive chemical reactions. 13. The reservoir computing method according to any one of the preceding claims, wherein the non-linear chemical process comprises one or more autocatalytic reactions. 14. A reservoir computing system comprising: a reservoir which is operable to output an output signal in response to an input signal, wherein the reservoir includes a reactor apparatus with a reactor chamber for receiving chemical substances and facilitating chemical reactions during a chemical process; an input layer having at least one input node configured to receive the input signal, wherein the at least one input node is associated to one or more process parameters and/or a quantity of one or more chemical substances provided to the reactor chamber; and a computer implemented trained output layer having at least one output node configured to output the output signal that is based on one or more readout outputs of the reservoir in response to the input signals. 15. Use of a trained reservoir computing system of claim 14 for characterizing an input signal.

Description:
Title: a method of reservoir computing and a reservoir computing system FIELD OF THE INVENTION The invention relates to a method of characterizing an input signal by means of reservoir computing. The invention also relates to a reservoir computing system. Also, the invention relates to the use of the system for characterizing an input signal. Additionally, the invention relates to a computer comprising a reservoir computing system. BACKGROUND TO THE INVENTION The field of machine learning aims to teach computer systems how to perform tasks on previously unseen data, without explicitly programming them (cf. procedurally). The arsenal of available machine learning techniques is comprehensive. Reservoir computing is a machine learning technique which has gained more popularity in recent time for dealing with information processing. It can find application in both the digital and the analog domain. In reservoir computing, a dynamical system, which is referred to as a computing reservoir is employed for computation. The reservoir is excited by the inputs to be processed and its output states are trained to follow a desired output, e.g., by linear regression, while keeping the computing reservoir itself untrained. Compared to artificial neural network machine learning models, the training process can be made significantly easier by employing reservoir computing. The computing reservoir itself acts as a nonlinear pre-processor which can project an input signal into a higher dimensional space where it becomes easier to classify, e.g., using a linear classifier or linear regression. Hence, this methodology can be used to ease artificial neural network training for solving a variety of complex problems. It is clear that the reservoir has significant impact on the reservoir computing system. The reservoir is preferably in the proper dynamical regime at the edge of instability, such that the system is dynamic enough without becoming instable. The implementation of the computing reservoir may be an important limiting factor in various applications. There is a need to offer a system which is relatively easy to use, combined with computational capabilities matching or exceeding other machine learning techniques, such as deep learning networks, for a broad range of applications. There is a strong need for providing reservoir computing systems with improved performance. SUMMARY OF THE INVENTION It is an object of the invention to provide for a method and a system that obviates at least one of the above mentioned drawbacks. Additionally or alternatively, it is an object of the invention to provide for improved reservoir computing. Additionally or alternatively, it is an object of the invention to provide for a more robust and/or accurate reservoir computing. Additionally or alternatively, it is an object of the invention to provide for a reservoir computing method that relies less on silicon-based computing, which are e.g. required to run simulations of reaction networks in silico. Thereto, the invention provides for a method of characterizing an input signal, the method comprising the steps of: providing a reservoir which is operable to output an output signal in response to an input signal; wherein the reservoir is provided with a reactor apparatus with a reactor chamber for receiving chemical substances and facilitating chemical reactions during a chemical process; conducting a non-linear chemical process inside said reactor chamber by providing one or more chemical substances to said reactor chamber, wherein said non-linear chemical process comprises one or more chemical reactions; providing an input layer having at least one input node configured to receive the input signal; wherein the at least one input node is associated to one or more process parameters and/or a quantity of one or more chemical substances provided to the reactor chamber; and providing a trained computer implemented output layer having at least one output node configured to output the output signal that is based on one or more readout outputs of the reservoir in response to the input signals. Advantageously, this physical reactor approach may significantly facilitate scaling. The reservoir computing may be more easily scalable for bigger problems. For example, if a larger network is required, it is possible to carry out the non-linear chemical process in the reactor for a longer period of time. If the non-linear chemical process is performed over a longer period of time, more connections may be formed, and an even larger set of outcomes per experiment may be analyzed. Such upscaling potential of the reservoir computing unit may be of vital importance for various machine learning problems. The reservoir computing system may be computer controlled. The reactor may have input parameters which influence the non-linear chemical process and output readouts which are converted to outputs by the trained output layer. The selection of the inputs and outputs may be done depending on the application of the reservoir computing system. More particularly, it may depend on the problem (cf. function approximation) and the input signal to be characterized. The reservoir computing according to the disclosure allows for easier training compared to for instance recurrent neural networks, and can be used for solving a variety of complex problems (e.g. time series prediction). For a system identification task, the reservoir computing system can be trained such that it mimics a given system. The internal operation or composition of the system to be identified is typically unknown. First a training input is applied to the system and the output is recorded. This forms an input/output training pair. The training input is then applied to the reservoir and node states over time can be recorded in a state matrix. The weights of the readout layer can be calculated, for example using a pseudo-inverse of the state matrix, such that a linearly weighted combination of the node states results in an output as closely matched to the training output as possible. After this training phase, the reservoir computer performs as the system to be identified, generalizing its response to previously unseen input signals. Advantageously, by employing a reactor reservoir with a reactor tank in which a non-linear chemical process takes place, a practical and economically sound implementation of a reservoir computing system can be obtained, since the non-linear chemical process provides for a large number of nodes connected to other nodes based on a chemical reaction network. This approach radically simplifies the construction of the reservoir of the reservoir computing system. Moreover, this provides an easy way for scaling up the reservoir computing system for handling more complex tasks. It will be understood that herein, “chemical process” is typically meant to indicate a non-linear chemical process, unless indicated otherwise. As is known to the person skilled in the art of chemistry, a chemical process comprises one or more chemical reactions. In the non-linear chemical process employed herein the non-linearity arises from the interplay between these chemical reactions. This can be achieved by chemical reactions that are non-linear by nature, a combination of linear chemical reactions that results in non-linear behaviour, and a combination thereof. Therefore, the non-linear chemical process employed in the invention preferably comprises one or more non-linear chemical reactions, and/or one or more combinations of chemical reactions yielding non-linearity. Thus, the non-linearity required for reservoir computing is provided. Such non-linear chemical reactions are well-known and well-studied in the art, and have been discovered in a large number of biochemical systems, and have been designed and performed by chemists as well. Similarly, non-linear combinations of chemical reactions are also known in the art. For example, an autocatalytic cycle, which is inherently non- linear, is formed in the well-known formose reaction from a series of linear reactions. Preferably, the non-linear chemical process as described herein relates to a chemical reaction network, wherein the one or more chemical substances and one or more chemical reactions together form an interconnected network. In such a chemical reaction network, the different reaction products may influence one or more of the chemical reactions occurring in the reactor, and thus may affect which products are formed, and/or the quantities of the products formed. It will be appreciated that various chemical reaction networks may be utilized. The reaction network may be a recursive network having one or more feedback loops. The reaction network is typically inherently non-linear. A well-known, and preferred non-linear chemical process is the formose reaction, which is also known as the Butlerov reaction. Therein, a vast amount of products can be formed from simple and readily starting materials, such as formaldehyde, a base (typically NaOH), and a divalent metal. As will be readily understood by the skilled person, the term “formose reaction” is used in the singular form for ease of reference, but it actually typically comprises a plurality of different chemical reactions which form a reaction network. Likewise, other chemical reaction networks may also be referred to by a singular term, such as the Briggs-Rauscher reaction. It is immediately apparent to the skilled person which set of chemical reactions is referred to in such a case. The products formed in the various reactions comprised in the formose reaction network may influence their own production, or the formation of further products. Therefore, the formose reaction network is recursive, and in fact any one of the possible reaction products may be used as a starting material, and vice versa. This presents a great advantage for applying such chemical reaction networks in the context of reservoir computing, since there are many different possible input variables, viz. input concentrations of a vast array of chemical substances, and reaction conditions such as temperature, pH, space velocity within the reactor chamber, etc. Still, all these conditions are easy to set, and readily lead to a large number of output products due to the non-linear nature of the chemical process, in particular of the chemical reaction network. The chemical composition of the reaction chamber can then be analyzed and quantified using standard analysis techniques. The concentrations of the various chemical substances in the reaction chamber can then be used as outputs of the reservoir computer. Various other chemical reaction networks are well-known in the art, and can all be employed in the present invention. These include, but are not limited to, the Briggs-Rauscher reaction, a trypsin-based oscillator (Semenov et al., Nature Chemistry, 2015, volume 7, pages 160-165), an oscillator based on small organic compounds (Semenov et al., Nature, 2016, volume 537, pages 656-660), supramolecular reaction networks, and nucleotide-based reaction networks (using DNA and/or RNA, both in vivo and in vitro). A review citing various chemical reaction networks is provided by Wong and Huck, Beilstein Journal of Organic Chemistry, 2017, volume 13, pages 1486-1497. All references are incorporated herein by reference. Optionally, at least one input node is associated to a quantity of the one or more chemical substances in the reactor chamber at the start of the non-linear chemical process. The starting chemical substance(s) may have a significant impact on the non- linear chemical process. In an example, a specific substance is used as starting material, and at least one substance is added during the non-linear chemical process (e.g. CaCl 2 and/or NaOH). The quantities of at least the added substances may be used as input parameters associated to the input signal to be characterized. These substances impact the output readouts and thus enable input signal discrimination. Optionally, the reactor chamber is in fluid communication with a plurality of substance interface ports for transport of chemical substances towards said reactor chamber during the non-linear chemical process, and wherein at least one input node is associated to a quantity of the one or more chemical substances provided to the reactor chamber. Optionally, at least one of the one or more chemical substances provided to the reactor chamber is a catalyst. For the chemical reactions to take place during the non-linear chemical process, various materials/substances (e.g. formaldehyde, glyceraldehyde, dihydroxyacetone) may be used. Additionally, one or more substances may be added during the non-linear chemical process. For example, catalysts may be added, such as but not limited to CaCl 2 and NaOH. These are particularly favorable if the non-linear chemical process is the formose reaction. CaCl 2 for example typically binds to the molecules that have two hydroxyl groups next to each other, and sodium hydroxide (NaOH) for example is a catalyst that can raise the pH value (resulting in the increase of the rate of some of the chemical reactions). These exemplary catalysts are two different catalysts that can affect different parts of the reaction network or different reactions in the reaction network. It will be appreciated that various other catalysts can be used, such as enzymes. Optionally, at least two chemical substances are provided to said reaction chamber, wherein at least a first chemical substance is a first catalyst and at least a second chemical substance is a second catalyst, wherein the first catalyst influences at least one first chemical reaction, and wherein the second catalyst influences at least one second chemical reaction, wherein the at least one first and second chemical reactions are different. The parameters (e.g. quantities of added substances; process parameters such as temperature, pressure, and acidity; etc.) that have an impact on the non-linear chemical process carried out inside the reactor may be chosen as input. Such input parameters may have impact on the output readouts, and therefore the output readouts can be differentiating as a result. By using parameters with strong influence on output readouts, the training the output layer of the reservoir computing system may be made more easy. However, parameters which induce less variation per small fluctuation in input, may provide a more robust output readout. The input parameters may be carefully chosen depending on the application/task of the reservoir computing. For example, temperature may have much less an effect on the non-linear chemical process than quantities of added substances such as the exemplary catalysts CaCl 2 and NaOH. Optionally, at least one input node is associated to one or more dynamic parameters of the one or more chemical substances provided to the reactor chamber. The physical reactor acts as the reservoir of the reservoir computing system. The computer controlled reservoir computing may define inputs which impact the non- linear chemical process in the physical reactor, and outputs which are determined by means of a trained output layer based on dynamic/changing readout outputs (e.g. measurement data indicative of substance quantities). The input may be dynamic, for example by varying in time the concentration of a chemical substance that is supplied to the physical reactor. These variations can be gradual or smooth, and can lead to a broad range of input concentration profiles, which may further increase the computing power of the reservoir. Optionally, these variations correspond to random variables generated from a probability distribution. Optionally, the one or more dynamic parameters is one or more oscillation parameters, wherein preferably the oscillation parameter is an amplitude of substance quantity and/or a frequency of oscillation. For example, it is possible to oscillate the concentration of a certain chemical substance as input (frequency and/or amplitude is input). Optionally, the reactor has one or more adjustable process parameters, and wherein a first set of adjustable process parameters are connected to the at least one input node, and wherein the one or more process parameters includes: pressure inside the reactor chamber; a space velocity of the chemical substances in the reactor chamber; a pH value inside the reactor chamber; and/or a temperature inside the reactor chamber. Optionally, values indicative of at least a subset of process parameters are connected to the at least one output node. Wherein the trained output layer is configured to convert said values (cf. output readout) into an output (e.g. a classification, prediction, etc.). Advantageously, the system can realize a complex nonlinear input/output characteristic. The chemical reactor based reservoir computing system can provide for a high energy efficiency solution for training the output layer of the reservoir computing model for extremely complex function approximations. Optionally, the one or more readout outputs of the reservoir are based on measured values including: one or more process states; data indicative of a reactor chamber compound composition; a number of different compounds in the reactor chamber; a concentration of one or more compounds in the reactor chamber; and/or relative differences in concentrations of different compounds in the reactor chamber. The networks of the computing reservoir (i.e. physical chemical reactor) do not need to be trained, because the reservoir can effectively produce an output based on its input. The input may be an excitation parameter influencing the non-linear chemical process being carried out inside the reactor (e.g. concentration of catalytic substance added, concentration of formaldehyde, pH value, etc.). The output layer may be trained such as to identify which transformation is to be carried on the measured/readout output (cf. monitored experimental process data). For example, the trained output layer may associate the measured/readout output to a trained classification output. In an example, the readout outputs may be (data indicative of) quantities of different molecules. The complexity of the information in the network of the reservoir can be dramatically increased when more output parameters (cf. readout outputs) are monitored. Furthermore, the reactor has not to be tuned, as the reactions of the non- linear chemical process depend on the reaction network. In some examples, the non- linear chemical process involves a formose chemical reaction network. Optionally, a plurality of outputs from the output layer are combined into one combined output. The combining may take into account a plurality of training parameters. Optionally, the one or more readout outputs of the reservoir are based on a rate of change of the measured values. Optionally, the non-linear chemical process comprises one or more non-linear chemical reactions. Optionally, the one or more chemical reactions of the chemical process span over multiple time scales. Optionally, the non-linear chemical process involves the formose reaction. In the formose reaction, sugars may be formed from formaldehyde. The reaction may be catalyzed by a base and a divalent metal such as calcium. Intermediary steps may take place, such as aldol reactions, reverse Aldol reactions, and aldose-ketose isomerizations. Intermediates are glycolaldehyde, glyceraldehyde, dihydroxyacetone, and tetrose sugars. Optionally, the non-linear chemical process carried out inside the reactor has a duration of at least 2 minutes, more preferably at least 60 minutes. In some examples, a first output is generated after a first time period, and a subsequent output is generated after a second time period, wherein the first time period is smaller than the second time period. In some examples, the second time period is at least 10 times larger than the first time period, more preferably at least 50 times larger, even more preferably at least 100 times larger. For example, a first output may be generated after a couple of minutes, and the subsequent output may be generated after a couple of hours, after a couple of days or even in some examples after a couple of weeks. It is also possible that a plurality of subsequent outputs are generated and monitored. Optionally, the system 1 is configured to collect, over time, a plurality of samples from the inside of the tank for determining one or more output readouts. The time period may be chosen for obtaining a steady-state response of the output readouts. When steady-state is reached, the output may remain substantially constant over time. For example, the time period (cf. duration of the non-linear chemical process) may be chosen based on the time needed for obtaining a steady-state response of substance concentrations. This time period may, inter alia, depend on the reactor volume and flow rate. For example, a relatively short time period may be required for reaching a steady-state of the output readout(s) when a relatively small physical reactor is used. Therefore, advantageously, a miniaturized reactor, such as a microfluidic flow reactor, may significantly reduce the time needed for reaching the steady state. Additionally or alternatively, a relatively high flow rate may be employed for accelerating the time needed for reaching steady-state. It is also possible to measure continuous changes of output readouts instead of steady state output readouts. Moreover, while the size of the physical reactor is not critical, a microfluidic flow reactor may also be advantageously used to lower the amount of substances used, since only small volumes are required. Still, the same information content can be achieved within the reservoir as with a much larger reactor. Optionally, the one or more chemical substances are selected from the group consisting of small organic compounds, proteins, synthetic polymers, and inorganic compounds. In relation to the invention, small organic compounds are molecules comprising at least one carbon-hydrogen bond. Preferably, the small organic compounds have a molecular weight of at most 2000 g/mol, more preferably at most 1500 g/mol, even more preferably at most 1000 g/mol, and most preferably at most 750 g/mol. For example, the small organic compounds may be selected from the group consisting of carbohydrates, peptides, peptoids, lipids, amino acids, and derivatives thereof. Carbohydrates may include monosaccharides, oligosaccharides, and polysaccharides. Preferably, especially if the non-linear chemical process is a formose reaction, small organic compounds are selected from the group consisting of formaldehyde, glycolaldehyde, dihydroxyacetone, erythrulose, and ribose. Optionally, one or more of the proteins is an enzyme. Enzymatic reaction networks are also well-known in the art, both synthetic enzymatic reaction networks and ones that occur in biological systems. Preferably, the protein is a protease, preferably a protease selected from the group consisting of trypsin, chymotrypsin, elastase, thrombin, thermolysin, proline-specific endopeptidase, and phosphatase. Advantageously, the proteases can be encapsulated in beads, preferably hydrogel beads, so that said proteases can be retained in a container, e.g. a microfluidic flow reactor. If the one or more substances used in the nonlinear chemical process comprises one or more proteases, it is preferred that said one or more substances also comprise one or more substrates of said proteases. Said substrates are typically peptides, proteins, or derivatives thereof, but peptides and derivatives thereof are preferred for ease of synthesis. Derivatives of peptides are for example phosphorylated peptides, and/or peptides that are coupled to a protease inhibitor. In the latter case, the activity of the protease inhibitor is severely decreased by coupling to the peptide, while it is reactivated by cleaving off the peptide moiety by a protease. Optionally, the reaction networks are not based on deoxyribonucleic acid (DNA). As such, the one or more chemical substances is preferably not DNA, and the synthetic polymers are preferably not DNA. In some examples, the inorganic substances are salts, that are typically dissolved in a solvent, such as the catalysts of the formose reaction, i.e. NaOH and CaCl 2 . Optionally, the substances are initially dissolved in a solvent. A preferred solvent is water, in particular aqueous buffers, but other solvents used for organic reactions can be used as well. These include, but are not limited to, dichloromethane, dimethyl sulfoxide, tetrahydrofuran, acetic acid, acetone, acetonitrile, benzene, butanol, butanone, chloroform, cyclohexane, 1,2-dichloroethane, diethyl glycol, diethyl ether, diglyme, 1,2-dimethoxyethane, dimethyl formamide, 1,4-dioxane, ethanol, ethyl acetate, ethylene glycol, glycerin, heptane, hexane, methanol, propanol, petroleum ether, pyridine, sulfuric acid, toluene, triethyl amine, xylene, and mixtures thereof. When aqueous solutions are used, the pH thereof depends on the non-linear chemical process used, and may vary over time or kept stable by the use of e.g. a buffer. The skilled person is well capable to select a suitable pH range for various chemical processes. In general, the pH of the aqueous solution used in the chemical process is in a range of from about 1.0 to about 13.0. For example, the formose reaction is preferably carried out under alkaline conditions, viz. at a pH of at least 7.0, more preferably at least 8.0. For biochemical processes, which e.g. include enzymatic reactions, the pH is typically in the range of from about 6.5 to about 8.5, more preferably in a range of from about 7.0 to about 8.0. However, in the autocatalytic urease reaction, for example, a starting pH of about 3.0 may be employed, after which the reaction products increase the pH. Similarly, the non-linear chemical process can be carried out at various different temperatures, depending on the nature of the chemical substances and the chemical reactions. The skilled person is well capable of selecting an appropriate temperature for a given chemical process. In general, temperatures of more than 0 °C are employed during the non-linear chemical process, more preferably in a range of from about 10 °C to about 85 °C, even more preferably in a range of from 15 °C to 60 °C, and most preferably in a range of from 20 °C to 40 °C. Likewise, the non-linear chemical process can be conducted using different residence times depending on the chemical process to be used. The residence time is defined as the total time that a fluid parcel has spent inside a control volume, viz. the reaction chamber. As used herein, residence time is typically used to indicate the mean residence time. Preferably, the residence time is at least 30 seconds, more preferably at least 60 seconds, and most preferably at least 100 seconds. The skilled person will know how to select the correct residence time, for example to allow the non-linear chemical process to reach a steady state within a practical amount of time. Another way of defining the flux within the reaction chamber is by using the space velocity, which is defined as the quotient of the entering volumetric flow rate of the reactants divided by the reactor volume. Optionally, the chemical process is a chemical reaction process involving a plurality of chemical reactions. Optionally, the non-linear chemical process comprises one or more recursive chemical reactions. Output products of reactions can in turn be input products for subsequent same or different reactions during the chemical process. Optionally, the non-linear chemical process comprises one or more autocatalytic reactions. The chemical process may involve at least one autocatalytic reaction resulting in a non-linearity which can be fully exploited by the reservoir computing. In an autocatalytic reaction, one of the reaction products is also a catalyst for the same or a coupled reaction. In addition, or alternatively, the non-linear chemical process optionally comprises one or more sets of collectively autocatalytic reactions. A set of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules. Autocatalytic reactions are well-known in the art and can be readily implemented in the present invention. Examples of autocatalytic reactions include, but are not limited to, the activation of trypsinogen by trypsin, the reaction of permanganate with oxalic ac id, the α-bro mination of acetophenone with bromine, the urease reaction in a solvent with lower buffer strength, and the like. Optionally, the non-linear chemical process may result in a greater number of output substances than the number of input substances. Different techniques may be used for generating the output readouts. For example, chromatography may be used for separating and/or identifying compounds from a mixture of substances. Various different chromatography methods may be used, such as for example gas chromatography, high performance liquid chromatography, gel permeation chromatography, gel filtration chromatography, etc. Various similar or different techniques may be used for keeping track of quantities of predetermined substances within the reactor, resulting from the non-linear chemical process. In some examples a spectroscopy technique is employed, such as fluorescence spectroscopy, absorption spectroscopy, emission spectroscopy, and/or nuclear magnetic resonance spectroscopy. Another technique to analyze, and in particular quantify, the contents of the physical reactor includes mass spectrometry. According to an aspect, the invention provides for a reservoir computing system comprising: a reservoir which is operable to output an output signal in response to an input signal, wherein the reservoir includes a reactor apparatus with a reactor chamber for receiving chemical substances and facilitating chemical reactions during a chemical process; an input layer having at least one input node configured to receive the input signal, wherein the at least one input node is associated to one or more process parameters and/or a quantity of one or more chemical substances provided to the reactor chamber; and a computer implemented trained output layer having at least one output node configured to output the output signal that is based on one or more readout outputs of the reservoir in response to the input signals. A physical reactor in which the non-linear chemical process is carried out is used as the reservoir. Retrieved experimental sampling data retrieved during the non- linear chemical process can be used for determining an output by means of the trained output layer. The chemical-reactor reservoir approach can provide stable and robust characterization of the input signal. The chemical reactor reservoir may provide an extremely flexible interconnection topology, offering improved scalability. A longer duration of the non-linear chemical process may result in the formation of more products resulting from the various chemical reactions. As a result, a larger complexity is achieved, which can be exploited by means of the reservoir computing system for handling more complex tasks on unseen data (e.g. classification). More particularly, during said non-linear chemical process, products formed as a result of one or more chemical reactions may be used in one or more subsequent chemical reactions. As a result, with a relatively small set of reactions carried out inside the reactor during the non-linear chemical process, a large diversity of products may be obtained. A reactor hardware platform is used in the reservoir computing, which can provide a substantial speed gain in training the machine learning model for complex tasks. Furthermore, the reactor does not require difficult technology, for example costly components, complex manufacturing processes, high cost of maintenance, etc. By contrast, simple equipment can be employed, which is commercially available or can readily be made in-house if desired. Similarly, chemical substances can be used that are abundantly available commercially, or can be readily synthesized if required. Optionally, the reactor used as reservoir is miniaturized. In some examples, the miniaturized reactor is arranged in an integrated reservoir computing system. In some examples, one or more sensors are arranged at the miniaturized reactor for providing output readouts. Additionally or alternatively, it is possible that the reservoir computing system comprises a cartridge with one or more substances, wherein the computing system may provide an amount of the one or more substances from the cartridge to the reactor based on input parameters. The reactor may have a plurality of interfaces for providing material to the reactor and/or removing material from the reactor. For example, the reactor may have one or more inlet ports, for example in fluid communication with the cartridge. The cartridge may be detachable, replaceable and/or refillable. Advantageously, the reactor may be used to keep the non-linear chemical process out-of-equilibrium during the desired duration of the chemical process. When the process is out-of-equilibrium, a thermodynamic equilibrium is typically not reached. To achieve this, the one or more chemical substances can be supplied to the reaction chamber through one or more, preferably at least two, inlets. The contents of the reactor chamber can then be flushed out through one or more, preferably one, outlet, after which the contents of the reaction chamber can be analyzed. Supplying the one or more chemical substances can be readily achieved by for example providing stock solutions of the one or more chemical substances in one or more containers, such as syringes, that are in fluid communication with the reaction chamber, and slowly transferring (a part of) the stock solution to the reaction chamber, for instance by the use of one or more pumps. In other advantageous embodiments, the non-linear chemical process is conducted under batch conditions. Then, the process may reach thermodynamic equilibrium if a long enough duration of the chemical reaction is selected. In such a case, the reactor can be any container for receiving chemical substances and facilitating chemical reactions during a chemical process, such as a beaker, flask, vial, and the like. Optionally, the reactor is a continuous-flow stirred-tank reactor configured to facilitate chemical reactions during the chemical process. Such continuous-flow stirred- tank reactors are particularly useful in keeping the non-linear process out-of- equilibrium. Optionally, the reactor is mixed and/or isothermally controlled. The tank may have one or more ports through which substances are added to the tank. For example, a stream of one or more substances may be fed into a tank volume and the one or more substances may react within the tank during the non-linear chemical process. The tank may further include an outlet through which fluid inside the tank can flow out. Various sensors may be used for retrieving output readouts during and/or after the non-linear chemical process. The sensors may perform online measurements or offline measurements. For the purpose of offline measurements, a sampling unit may be provided which is configured to retrieve samples from the inside of the tank. According to an aspect, the invention relates to a use of a chemical reactor in a reservoir computing system for characterizing an input signal. According to an aspect, the invention relates to a use of a trained reservoir computing system of the disclosure for characterizing an input signal. The reservoir computing system may present an alternative approach to the existing neural network configurations, such as recurrent neural networks (recurrent neural networks (RNN), long short-term memory networks (LSTM), etc.). It will be appreciated that reservoir computing describes a broad range of recurrent neural networks, including liquid state machines and echo state networks. Reservoir computing uses a collection of recurrently connected units called a reservoir. Inputs are accepted by the reservoir and mapped to a higher dimension. The state of the reservoir can then be read to determine the desired output. Reservoir computing offers the potential for efficient parallel processing and nonlinear signal discrimination. For example, reservoir computing can be used to efficiently solve a number of tasks that are deemed computationally difficult, such as identifying features images, predicting chaotic time series, and speech recognition. It will be appreciated that any of the aspects, features and options described in view of the method apply equally to the system and the described use. It will also be clear that any one or more of the above aspects, features and options can be combined. BRIEF DESCRIPTION OF THE DRAWING The invention will further be elucidated on the basis of exemplary embodiments which are represented in a drawing. The exemplary embodiments are given by way of non-limitative illustration. It is noted that the figures are only schematic representations of embodiments of the invention that are given by way of non-limiting example. Fig. 1 shows a schematic diagram of a system. Fig. 2 shows a schematic diagram of a system. Fig. 3 shows a schematic diagram of a process. Fig. 4 shows a schematic diagram of exemplary function approximations. Fig. 5 shows a schematic diagram of a process. Fig. 6a-d show schematic diagrams of different representations related to reservoir computing properties of the formose reaction. Fig. 7 shows schematically how the formose reaction is used as a reservoir computer to model a specified driven dynamic system. Figure 8a-d depict an example of a dynamic flow experiment used to predict a driven delay difference equation. Figure 9a-b relate to reservoir computing using a nonlinear protease reaction network. DETAILED DESCRIPTION Fig. 1 shows a schematic diagram of a reservoir computing system 1. The system 1 comprises a reservoir 3 which is operable to output an output signal 5 in response to an input signal 7. The reservoir 3 includes a reactor apparatus with a reactor chamber 9 for receiving chemical substances and facilitating chemical reactions during a chemical process. The system 1 comprises an input layer 11 having at least one input node 13 configured to receive the input signal 7, wherein the at least one input node 13 is associated to one or more process parameters and/or a quantity of one or more chemical substances provided to the reactor chamber 9. The input layer 11 may transform the input signal 7 into input parameters 10 provided for setting/adjusting said one or more process parameters and/or quantity of one or more chemical substances provided to the reactor chamber 9. Furthermore, the system 1 comprises a trained output layer 15 having at least one output node 17 configured to output the output signal 5 that is based on one or more readout outputs 19 of the reservoir 3 in response to the input signals 7. Advantageously, more complexity can be easily obtained using the chemical reactor as reservoir for the reservoir computing system 1. Moreover, the obtained complexity can be easily scaled up. For example, scaling can be achieved by increasing a duration of the chemical process inside the reactor. Moreover, the reservoir computing system 1 provides for a very robust design. The initial starting substances used in the reactor may have great impact on the non-linear chemical process. For example, the starting substances may be formaldehyde, glyceraldehyde, and/or dihydroxyacetone. The input layer may be configured to receive the signal to be characterized as input and translate this signal to data indicative of the quantitative ratios of the starting substances. This data can then be used for controlling one or more configurations of the reactor such as to influence the non-linear chemical process. Additionally or alternatively, the input layer may be configured to translate the input signal to data indicative of a concentration of additives during the process in the reactor. The additives may for instance be catalysts. Additionally or alternatively, the input layer may be configured to translate the input signal to data indicative of a dynamic change (e.g. oscillation) of added substances. Additionally or alternatively, the input layer may be configured to translate the input signal to data indicative of one or more process parameters (temperature, pressure, pH, etc.). The non-linear chemical process inside the tank may involve a chemical reaction network that is capable of exhibiting multiple steady state behavior, or a hysteresis, causing a large difference in the yield of some product in response to a small perturbation in a reacting species’ concentration or flux. Under certain conditions, a reaction network might not reach any steady state at all, but instead experience sustained oscillatory behavior. Such behavior may also be exploited by the reservoir computing system according to the disclosure. Fig. 2 shows a schematic diagram of a system 1. The reservoir 3 is a chemical reactor in which a non-linear chemical process occurs. For illustrative purposes, possible reactions within the formose reaction network are depicted. As described herein, other chemical reaction networks may also be employed. The chemical reactions may be recursive, thus resulting in non-linear output readouts provided to the output layer 15. Advantageously, the reservoir computing system provides for improved nonlinear signal discrimination. The reservoir computing system uses a collection of recurrently connected units called a reservoir. According to the invention, the units within the reservoir computing system are the chemical reactions which occur in the reactor. Hence, the reservoir computing system is based on a non-linear chemical process and employs a physical reactor (i.e. hardware) for facilitating the chemical process. Advantageously, the reservoir computing system uses the reactor reservoir to propagate a signal component therein in a complex manner, in order to learn a complex input/output characteristic. The reservoir computing system learns weights of an output mechanism, without changing the weights of the input mechanism and the weights inside the reservoir which is a physical reactor device that outputs a nonlinear output readout in response to an input. The reactor reservoir, in which a non-linear chemical process occurs, provides a strong nonlinearity and is thereby well suited for various complex machine learning tasks. The reservoir computing system can be trained by modifying only a small amount of variable weights of the output layer, leading to an advantage in low learning cost whilst being able to handle complex problems. Moreover, the reservoir computing system according to the disclosure enables easy scaling up for increased complexity. In some examples, the tank includes a plurality of controllable valves for controlling the flow of chemical substances. The reactor tank may comprise various arrangements for further facilitating the chemical reactions inside the tank during the non-linear chemical process. For instance, the tank may comprises a light source, an optical stimulation, a vibrator, an acoustic transducer (vibrations), a sonic vibrator, a heater/cooler, a mixing device, etc. Fig. 3 shows a schematic diagram of an exemplary process in which the reservoir computing system according to the disclosure is used for a XOR-function approximation. Two input parameters are used (x-y axis). In this example, concentrations of NaOH and CaCl 2 are used as input parameters (a). However, various other input parameters can be used which influence the non-linear chemical process. The input parameters may be parameters which can be changed for affecting the non-linear chemical process for example. As a result of the input parameters, the concentrations of NaOH and CaCl 2 added to the chemical reactor are selected. This will affect the non- linear chemical process in the chemical reactor (b) and result in certain output readouts (c). The output layer is trained to convert said output readouts to a final output, in this case approximating the XOR-function. Fig. 4 shows a schematic diagram of a process in which the reservoir computing system 1 according to the invention is employed for performing a machine learning task. In this example, a continuous stirred tank reactor is employed, with four inputs and one output. It will be appreciated that various other configurations are possible. An exemplary schematic overview of reaction pathways enabled inside the reactor is illustrated. Furthermore, a general workflow to obtain computational results is illustrated, wherein the detected concentration of every component in the network is multiplied with trained weights. These are then summed to obtain the final output value (either 0 or 1, or a continuous value, depending on the specific problem). In this example, the formose reaction is employed to establish a chemical reaction network capable of reservoir computation. Sugar-forming reactions in the formose system use formaldehyde as a C1 building block, and dihydroxy-acetone (DHA) or other initiator sugars as C2-C5 building blocks. Under the influence of catalysts such as hydroxide and Ca 2+ five separate reaction-classes are enabled: enolate formation/protonation, aldol addition, retro-aldol reactions, and Cannizzaro reactions. Recursive application of these reaction classes to the basic Cn building blocks leads to a combinatorial explosion of sugar-like compounds. To ensure the system is out-of- equilibrium, the reactions are run in flow inside a continuous stirred-tank reactor (CSTR). This flow-setup allows for easy modification of the input variables: the input concentrations of buildings blocks (formaldehyde, DHA) and catalysts (NaOH, CaCl 2 ). Output of the system is sampled in fractions from the reactor outflow and, after derivatization, analyzed by GC-MS (gas chromatography / mass spectrometry) and HPLC (high-performance liquid chromatography). Analysis of chromatographic peaks and mass spectra then allows for quantification of the chemical composition, for which 52 separate compounds have been detected in the output mixtures and determine the respective concentrations. Finally, these concentrations are used as outputs of the reservoir computer. The reservoir computation performed by means of a physical chemical reactor provides for adequate complexity and dynamic response. The reactor provides for an advantageous black-box reservoir, from which the final output is obtained for example by combining outputs of the reservoir in a linear fashion (cf. output layer). The reservoir computing system according to the disclosure provides for a sufficiently complex reservoir which holds similar or even improved computational power compared to regular artificial neural networks, while being much more efficient due to far fewer parameters that need to be tuned or trained. Advantageously, the physical reactor reservoir in which chemical processes occur, provides a high-dimensional internal state space, nonlinear interactions, fading memory, and sufficient separation and generalizability of input signals. For example, it is shown in the Examples that prebiotic formose networks in flow conditions exhibits features of a reservoir computer, and that it allows to perform nonlinear classification tasks and universal function approximation on its input by making simple, linear combinations of its output concentrations. Fig. 5 shows a schematic diagram of exemplary function approximations. More particularly, a nonlinear classification and function approximation is shown. In (a) a specification of the XOR classification decision boundaries on input space is shown. In (b), the trained weights obtained by linear regression on full dataset is shown. In (c), the output obtained by application of the trained weights is shown. In (d), the specification of a Bessel function that encodes the u22 vibration mode of a circular membrane on the input space is shown. In (e), trained weights obtained by linear regression on a full dataset is shown. In (f), the output obtained by application of the trained weights is shown. In order to test the computational capacity of the formose reservoir computer, a nonlinear classification of input variables has been implemented in an example. Specifically, an XOR-gate and other (nonlinear) classification behaviour is shown. Here, the input concentrations of catalysts NaOH and CaCl 2 function as continuous input variables that need to be classified according to a nonlinear decision boundary. By performing a linear regression on a full dataset of output concentrations, weights are obtained which can be used on individual output points to calculate a weighted sum of concentrations. This procedure is shown in (a-c), and can successfully classify the environmental inputs as either 0 or 1 according to XOR-gate decision boundary. By increasing the number of available datapoints to calculate the weights from, essentially increasing the size of the training data, the precision of the decision boundaries is increased and the accuracy of predictions in the input space is improved. This accuracy of predictions was further checked and verified by cross-validation on every point in the dataset. The classification of inputs (environments) happens entirely inside the formose system (cf. chemical reaction in the reactor), where essentially a nonlinear projection to a high-dimensional space (of compound concentrations) takes place. Because the final step of the calculation is a linear transformation, it does not contribute meaningfully to the computational power of the nonlinear classification. Moreover, the same data can be used to perform many different types of classification. Alongside all Boolean classification problems (AND, OR, XOR, IMPLY), the system is capable of classifying input according to arbitrary decision boundaries. The reservoir computing system can be used for various function approximations. In order to show the capacity of the formose reaction to approximate any function, the same dataset and procedure is used to approximate different vibration modes of a circular membrane (given by the spherical Bessel functions), an example of which is shown in (d-f). The spherical Bessel functions form a complete basis for continuous functions on a defined interval. Similarly, since weights are obtained by means of a linear regression, a simple linear combination of weights corresponding to specific Bessel equations is equivalent to creating a linear combination of those Bessel functions themselves. Thus, in the case of two changing input variables, the system operates equivalently to a universal function approximator for functions of two variables. Importantly, all classifications and approximations can be performed simultaneously in the same system. The final results can be obtained by only changing the readout weights according to which computation is required. Fig. 6a-d show schematic diagrams of different representations related to reservoir computing properties of the formose reaction. Fig. 6(a) illustrates that a combinatorial explosion of number of components through nonlinear interactions leads to a strongly recursive complex network. Fig. 6(b) illustrates a self-organization of the reaction network under the influence of environmental changes. Fig. 6(c) shows a schematic of high-dimensional separation of inputs in the chemical state space. Fig. 6(d) shows a nonlinear classification of inputs by linear separation in chemical state space. The origin of the high information processing capacity observed in the formose system stems directly from the capability of the network to self-organize its reactivity in response to different environmental conditions, while creating and maintaining a large number of distinct chemical species. Because all of these chemical species are capable of undergoing reactions with each other, aided by the inclusion of catalysts, a strongly recursive network of nonlinear reactions emerges, see e.g. fig.6(a). Changing environments (e.g. changing computational inputs) establishes a collective change in the composition of the network by favoring reactivity in different parts of the overall network, see e.g. fig. 6(b). Essentially, changing inputs establishes a change in interactions between different parts of the network, which results in the system effectively mapping the low-dimensional input space to its internal high-dimensional state space, see e.g. fig.6(c). Due to the large number of components, every classification or approximation task can correspond to a different subset of relevant components that is picked up by the linear regression algorithm, or rather, a linear low-dimensional manifold inside the high-dimensional state space, see e.g. fig.6(d). Therefore, solving any classification problem simply constitutes choosing appropriate weights for every component in the system. This contrasts with previous methods of performing computations in chemical reaction networks, where often a single component (or unchanging set of components) is chosen as relevant output. Instead, it has been observed that by considering the full system response, the computational capacity becomes much more powerful. Fig.7 shows schematically how the formose reaction is used as a reservoir computer to model a specified driven dynamic system. The input signal is used both as a drive for the dynamic system, and (transformed) as a chemical input to the formose system. Weights are computed by fitting the resulting timeseries of chemical concentrations for each chemical in the system to the desired target data, using a standard regression technique. New behaviour of the driven dynamic system can be predicted by presenting the formose reaction with a new part of the input signal, after which the previously acquired weights are applied to generate the prediction. Figure 8 depicts an example of a dynamic flow experiment used to predict a driven delay difference equation. Panel a) relates to a flow profile is generated from a normal distribution centered around 1.0 with standard deviation 0.2. While the flow profile is continuously varied, the CSTR of the formose system is only sampled approximately every 30s. These samples are divided into a train and test set as indicated. Panel b) shows an example of the resulting timeseries of the GCMS integrals of every component detected in the collected samples. Panel c) depicts the pre-calculated target value generated by a delay difference equation, driven by the normalized input signal. The train dataset is fitted to the target values by calculating the appropriate weights for every component detected in the data, using linear regression. The trained weights are then used on the test dataset to predict the remaining behaviour of the driven delay difference equation. Panel d) shows the residual errors for every train and test datapoint, calculated as the normalized root-mean-squared error. Figure 9 relates to reservoir computing using a nonlinear protease reaction network as described in Example 3. Panel a) schematically shows the basic principle of the protease reservoir computing system. Syringes filled with mixtures of peptides are used as inputs into a CSTR, which contains a collection of polyacrylamide beads functionalized with different proteases. The enzymes and substrates form a enzymatic reaction network with cross-interactions and inhibitions, resulting in a strongly nonlinear chemical process. In this system, the input peptides are converted into a mixture of many different peptides, which can be quantified using standard HPLC methods. Panel b) depicts an example of a nonlinear classification task performed by a protease reservoir computing system. The system receives four different input concentrations, corresponding to the four possible inputs for an XOR logic gate. The four inputs generate four different peptide concentration datasets, as obtained by peak integrals of HPLC measurements. These datasets are then used to train weights and obtain a correct nonlinear classification of the inputs. It will be appreciated that the method may include computer implemented steps. All above mentioned steps can be computer implemented steps. Embodiments may comprise computer apparatus, wherein processes are performed in computer apparatus. The invention also extends to computer programs, particularly computer programs on or in a carrier, adapted for putting the invention into practice. The program may be in the form of source or object code or in any other form suitable for use in the implementation of the processes according to the invention. The carrier may be any entity or device capable of carrying the program. For example, the carrier may comprise a storage medium, such as a ROM, for example a semiconductor ROM or hard disk. Further, the carrier may be a transmissible carrier such as an electrical or optical signal which may be conveyed via electrical or optical cable or by radio or other means, e.g. via the internet or cloud. Some embodiments may be implemented, for example, using a machine or tangible computer-readable medium or article which may store an instruction or a set of instructions that, if executed by a machine, may cause the machine to perform a method and/or operations in accordance with the embodiments. Various embodiments may be implemented using hardware elements, software elements, or a combination of both. Examples of hardware elements may include processors, microprocessors, circuits, application specific integrated circuits (ASIC), programmable logic devices (PLD), digital signal processors (DSP), field programmable gate array (FPGA), logic gates, registers, semiconductor device, microchips, chip sets, et cetera. Examples of software may include software components, programs, applications, computer programs, application programs, system programs, machine programs, operating system software, mobile apps, middleware, firmware, software modules, routines, subroutines, functions, computer implemented methods, procedures, software interfaces, application program interfaces (API), methods, instruction sets, computing code, computer code, et cetera. Herein, the invention is described with reference to specific examples of embodiments of the invention. It will, however, be evident that various modifications, variations, alternatives and changes may be made therein, without departing from the essence of the invention. For the purpose of clarity and a concise description features are described herein as part of the same or separate embodiments, however, alternative embodiments having combinations of all or some of the features described in these separate embodiments are also envisaged and understood to fall within the framework of the invention as outlined by the claims. The specifications, figures and examples are, accordingly, to be regarded in an illustrative sense rather than in a restrictive sense. The invention is intended to embrace all alternatives, modifications and variations which fall within the scope of the appended claims. Further, many of the elements that are described are functional entities that may be implemented as discrete or distributed components or in conjunction with other components, in any suitable combination and location. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word ‘comprising’ does not exclude the presence of other features or steps than those listed in a claim. Furthermore, the words ‘a’ and ‘an’ shall not be construed as limited to ‘only one’, but instead are used to mean ‘at least one’, and do not exclude a plurality. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to an advantage. EXAMPLES Example 1 – a formose reservoir computing system Instrumentation: HPLC analyses were performed on a Shimadzu Nexera X2 instrument. Conditions: GIST C18 column (2 µm pore size, 75 x 3.0 mm), 40 °C, 0.8 mL min. -1 , acetonitrile:water (1:1, 0.1% trifluoroacetic acid), 1 µL injection volume, UV-vis detection at 364 nm, or GWS C18 column (5 µm pore size, 250 x 4.6 mm) at 1.0 mL min. -1 , 40 °C, 1.0 mL min. -1 , acetonitrile:water (1:1, 0.1% trifluoroacetic acid), 1 µL injection volume, UV-vis detection at 364 nm. Gas chromatography-mass spectrometric analyses were performed on a JEOL JMS-T100GCv. Gas chromatography conditions: Agilent 7890A gas chromatograph; HP-5MS column, 30 m length, 0.250 mm diameter, 0.25 mm film thickness, He carrier gas, 1 mL min. -1 , 1 µL split injection (1/10), injector temperature 250 °C. Temperature program: Oven Temp/ °C: 100, 170, 210, 250, 325, Rate/ °C min. -1 : 0, 14, 4, 15, 60, Time/ min.: 2.33, 0, 0, 0, 3.75. Mass spectrometer conditions: JEOL AccuTOF mass spectrometer, Electron Impact Ionisation mode, Ionisation Voltage 2300 V, sampling rate 10 Hz. Flow reactions: A continuous stirred-tank reactor (CSTR, volume: 411 µL or 439 µL) with five inlets and an outlet was fabricated from polydimethylsiloxane as previously reported. 1 Cetoni Nemesys syringe pumps with Hamilton syringes were used to control input flow rates. Five stock solutions were prepared, viz. of CaCl 2 , NaOH, water, formaldehyde, and glyceraldehyde. Each stock solution was taken up into a syringe, and the syringes were mounted onto the syringe pumps. Individual flow rates were set for every syringe to achieve the desired starting concentration of each component inside the reaction chamber, as well as the desired residence time. In this example, a residence time of 120 seconds was chosen. The CSTR was kept at 21°C by connecting a copper tubing partially surrounding the CSTR to a water bath that was kept at the desired temperature. The starting concentrations of glyceraldehyde and formaldehyde in the reaction chamber were 200 mM and 50 mM, respectively. During the non-linear chemical process inside the reaction chamber, the starting concentrations of CaCl 2 and NaOH were varied as indicated below in Table 1. These variations were achieved by altering the rate at which the stock solutions of these chemical substances were supplied to the CSTR. To maintain the desired residence time, the rate of the water supply to the CSTR was altered to compensate. The content of the reaction chamber was allowed to continuously flow out of the outlet. For each set of starting concentrations of CaCl 2 and NaOH a sample of the outflowing contents was taken at one or more time points, e.g. after the non-linear chemical process had reached a steady state. This sample was then further analyzed by HPLC and GC-MS as further described below. After the final sample was taken, the flow rates of CaCl 2 and/or NaOH, and water were adjusted again to achieve another combination of starting concentrations. Table 1. Different combinations of starting concentrations of CaCl 2 and NaOH used. Derivatisation: Derivatisation for HPLC was performed similarly to a previously reported method. 2 Samples from the CSTR outlet (35 µL) were dropped directly into a solution consisting of DNPH saturated acetonitrile (300 µL), acetonitrile (97.5 µL), water (65 µL) and HCl solution (2 M, 2.5 µL). The solutions were incubated for at least 30 minutes before HPLC analysis. Derivatisation for GCMS analysis was performed according to reported procedures. 2–4 Samples from the flow reactor outlet (35 μL) were flash-frozen in liquid nitrogen and freeze-dried overnight to give dry to oily residues. To each sample was added a solution of O-ethylhydroxylamine hydrochloride in pyridine (75 μL, 20 g L -1 ). A solution of dodecane and tetradecane (100 μL, 1.6 mM each in pyridine) was then added to each sample. The samples were then shaken at 70 °C for 30 minutes. After cooling to room temperature, N,O-bis(trimethylsilyl)trifluoroacetamide (25 μL) was added to each sample. The samples were again shaken at 70 °C for 30 minutes. The samples were then cooled to room temperature, followed by centrifugation (3-5 min, 10,000 rpm). The supernatants were decanted into sample vials for analysis by GC-MS (see instrumentation section). Chromatographic data processing: Peak integration and assignment of raw chromatographic data was performed using a program written in the programming language Python with the packages NumPy 5 and Scipy. 6 Peaks were detected using the first derivative of chromatograms and their integrals were determined using the NumPy function trapz() with subtraction of a baseline linearly interpolated between the beginning and the end of the peak. Peak assignments were performed via comparison to reference samples, or via interpretation of peak mass spectra (calibrated samples match known fragmentation patterns) 7 and retention times, aided by inference from experimental data. Integrals were converted to concentrations using quadratic calibration lines. When authentic samples were not available, calibrations were estimated by averaging the calibration factors of compounds of similar carbon chain length to the uncalibrated compound (in cases where two peaks were observed for a compound, the calibration for the peak with the larger integral was used). Training of Reservoir Computer: Training of the output weights for the reservoir computer was performed using programs written in the programming language Python with the packages NumPy 5 , SciPy 6 , Pandas 8 , and Scikit-learn 9 . Experimental conditions and resulting concentration profiles were loaded into dataframes from CSV files. Then, specific to the computational problem to be trained, relevant experiments of specific experimental conditions were assigned the desired computational output: 0 or 1 for binary classifications, a continuous value for function approximations. A Scikit-learn linear regression model was then created (using the class sklearn.linear_model.LinearRegression), and the averaged concentration profiles of the experiments were fitted as a matrix of training data to a vector of desired outputs (using the fit(X,y) class method). This is equivalent to an ordinary least-squares linear regression, where X and y respectively denote a matrix of training data and a vector of target outputs, and the equation y = Xw is solved for the weights w. The trained weights can then be used on further experiments to calculate the outcome of the calculation performed by the formose network. Leave-one-out cross validation: To verify the robustness of the computations performed by the formose reservoir computer, leave-one-out cross validation was performed on all computational problems. This was done by recalculating the trained weights from datasets with one experiment left out, and then using the obtained weights to predict the outcome from the left-out experiment. This procedure was repeated for every experiment in the dataset, after which the correctness of predictions was scored. The accuracy of the formose reservoir computer was calculated as the average correctness of predictions in a leave-one-out cross validation of a full dataset. Results: the results of the reservoir computing method are shown in, inter alia, Figures 3 and 5. Conclusions: the present example shows that the formose reaction acts as a reservoir that can be used for reservoir computing. In the present example, certain conditions are chosen that are in no way critical for the method of the invention to work. Instead, other starting concentrations can be selected, as well as different flow rates, temperatures, and chemical substances supplied to the reactor chamber. Similarly, while the formose reaction is a particularly preferred system, the method of the invention can also be carried out with any other non-linear chemical process. The skilled person would know which chemical substances to supply to the reaction chamber to conduct any given non- linear chemical process. Example 2 – Prediction of driven dynamic systems with a formose reservoir computing system Figure 7 schematically shows how the formose reaction is used as a reservoir computer to model a specified driven dynamic system. Methods - Dynamic flow reactions Experiments were performed with time-varying input concentrations of respectively CaCl 2 , NaOH, formaldehyde, and dihydroxyacetone, to the nonlinear chemical process. The input concentrations and corresponding input flowrates were generated from a random noise distribution and updated every 1.022 seconds, such that the non-linear chemical process never reached steady state. This random noise distribution was generated from a normal distribution with a mean of 1.0 and a standard deviation of 0.2, and mapped onto the input concentrations by a linear transformation such that the mean corresponds to concentrations of 30 mM (NaOH), 150 mM (CaCl 2 ), 50 mM (dihydroxyacetone), and 100 mM (formaldehyde), and 0 corresponds to 0 mM. Other experimental conditions were equivalent to the experiments performed when collecting steady state data. For each experiment, samples of the outflowing contents of the nonlinear chemical process were taken approximately every 30 seconds, and subsequently further analyzed by HPLC and GC-MS as further described elsewhere. Methods - Prediction of driven dynamic systems Data obtained from the dynamic flow reactions described above were used for prediction tasks on driven delay difference equations and driven ordinary differential equations. For every experiment, data was first split into a training set and test set, with the first 100 samples in the training set, and the remainder in the test set. Then, specific to the driven dynamical system to be predicted, the same random noise used to obtain the training data from the non-linear chemical process was used to calculate the expected outcome of the dynamic system by integration of the corresponding differential equations. A Scikit-learn ridge regression model was then created, and the training data were fitted to the expected outcome of the dynamic system. This resulted in a set of trained weights, which were subsequently applied to the test data to predict the remainder of the dynamical system. Residual errors of this prediction were calculated using the normalized root mean squared error. Results – Prediction of driven dynamic systems Figure 8 shows an example of a prediction task for a driven delay difference equation. In this specific task, a second-order dynamic nonlinear transfer function was used as dynamic system: Where u(t) is the random noise input at time t, Δt the delay time, and y(t) the output of the dynamic system at time t. Applying the random noise input u(t) to the CaCl 2 chemical input of the formose reservoir computer results in a continuously varying chemical output, as shown in figure 8b. Figure 8c shows the true, expected output value of the delay difference equation (blue line), as well as the reconstructed output values after training (orange dots), and the predicted output values using the weights obtained from training (green crosses). Generally, the formose reservoir computer is able to reconstruct and predict the output of the delay difference equation directly from the random noise input, with maximum residual errors of ~0.015. As expected, the residual errors on the predictions are on average slightly larger than those of the reconstructed training output (Figure 8d). Different delay difference equations or ordinary differential equations, of the form can be approximated and predicted in a similar manner. Example 3 – Nonlinear classification with protease reservoir computing Figure 9a shows a schematic diagram of a reservoir computing system using encapsulated proteases and mixtures of peptides as input, to establish a nonlinear chemical process capable of reservoir computation. Enhanced nonlinearity is achieved by the potentially inhibiting interaction between different peptides and proteases, as well as sequential proteolysis of the initial peptides into a high number of different smaller peptides. It was shown that the protease network in flow conditions exhibits features of a reservoir computer, and that it allows to perform nonlinear classification tasks and universal function approximation on its input by making simple, linear combinations of the output concentrations of all resulting peptides. Figure 9b shows a schematic diagram of an exemplary nonlinear classification task, specifically a specification of the XOR classification decision boundaries on input space is shown. Here, the input concentrations of mixtures of peptides function as input variables that need to be classified according to a nonlinear decision boundary. The training procedure to obtain weights for the concentrations of different peptides is similar to previously described. Methods - Flow reactions with encapsulated enzymes A continuous stirred-tank reactor (CSTR, volume: 110 µL) with one inlet and one outlet was filled with enzyme-functionalized polyacrylamide beads, similar to a previously reported experimental setup (M.G. Baltussen et al., "A Bayesian Approach to Extracting Kinetic Information from Artificial Enzymatic Networks." Analytical Chemistry 2022, volume 94, pages 7311–7318. doi:10.1021/acs.analchem.2c00659). Cetoni Nemesys syringe pumps with Hamilton syringes were used to control input flow rates. The reactor was filled simultaneously with 7 different enzyme-functionalized beads, specifically Trypsin, Chymotrypsin, Elastase, Thrombin, Thermolysin, Proline-specific Endopeptidase, and Phosphatase. The inventors believe that the enzyme concentration and/or enzymatic activity is not critical and can be varied over a broad range. Two stock solutions of peptides were prepared, with solution I containing 4 peptides: CCFSWRCRC, SSVRWWSDDEWRW, AVNIPFKVHLRCKAAFC, and Ac-TKIFKI-NH2. Solution II contained 3 peptides: CCF(pS)WRCRC, TTMHPRL, and IYPFVEPI. All peptides were present in a 400 µM concentration. The two stock solutions were taken up into different syringes, and a third syringe was prepared with a Tris/Ca 2+ buffer solution. The three syringes were mounted onto the syringe pumps and connected to the CSTR. Input flowrates for every syringe were set to achieve the desired starting concentration of each component inside the reaction chamber, as well as the desired residence time. 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